Table of Contents
Single Pole IIR Impulse Response
The single pole infinite impulse response (IIR) filter is an incredibly efficient filter!
The impulse response of the single pole IIR is
The filter uses two weights, and . The weight is applied to the input signal x[n] and the value is typically small ( < 0.1 ). The weight is much larger than and is applied to the feedback y[n-1]. The smaller the the more impact the feedback has on the output and the smoother (and more narrowband) the filter.
The single pole IIR may also be referred to as an exponential moving average (EMA) filter.
Single Pole IIR Frequency Response
Equation (2) is simplified by gathering like terms,
The transfer function for (1) is written as the ratio of Y(z) to X(z),
The frequency response is created by substituting
into (5) resulting in
Simplify (7) by definining
such that the frequency response is now
Magnitude of the Frequency Response
The magnitude and phase of the frequency response (9) is given below. The plots show that as decreases the filter becomes more narrowband and has more phase linearity.